Abstract
In this paper kernel estimators for the stationary density of a homogeneous Markov chain with an arbitrary initial distribution are considered under the assumption (D 1) which is weaker than Doeblin’s condition (D 0 ). Condition (D 1) includes periodic Markov chains with cyclic subclasses and an unessential set. Convergence in probability, a.s. convergence and convergence in quadratic mean of these estimators are studied. In this paper estimations for MSE and MISE are given.
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